What is the Origin of the QR Reduction Formula?

8/25/2025

Regarding the QR sprinkler reduction: where does the -3 formula slope come from and where does the +55 come from in the equation Y= -3x /2 +55?

I've asked a few designers and they don't know. They said it is just something that is "Baked in," much like the Hazen-Williams formula, which includes elements we just accept.

However, I'm just curious and like knowing things like that. Thanks for any help.

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8 Comments

Pete H

8/25/2025 06:27:57 am

Source is AI, so take it with a grain of salt:

"The formula for design area reduction in fire sprinklers originated from fire testing conducted in the 1970s and 80s by FM and other organizations. This research demonstrated that quick-response sprinklers could suppress fires earlier, allowing for a reduction in the hyduralically calculated area compared to standard response sprinklers."

https://www.meyerfire.com/blog/calculate-the-quick-response-area-reduction#:~:text=The%20concept%20behind%20reducing%20the,of%20sprinklers%20needed%20to%20activate.

Additionally this meyerfire blog link has relevant information.

Anthony

8/25/2025 07:50:37 am

Can't comment on the QR formula but to "baked in" and "just accept" portion of the post I would say the following: Empirical formula are based on observed data and a best "fit line" is added. Goes like this: get a bunch of data points, as many as you can, and draw a line that best describes those plotted data. That line can be expressed as formula. So the -3 and +55 don't "mean" anything they are an expression of the data and create the best fit line in the units used.

Unknowingly you do the exact same thing with water flow tests. The line that you draw from static to residual is a "best fit line" it could also be expressed as an equation. (would be great if you had more than 2 data points but that's a brief look into data accumulation and funding issues) IF you want to have fun with this look up excel trend line fit and watch some videos. Or check out some data analytics classes at a local college or upskill site.

Josh

8/25/2025 08:12:11 am

This is the correct answer to the question about the numbers. The trendline will always have a formula associated with it.

By the time these formulas reach us in the working world, the research has been thoroughly done in universities and research companies, peer reviewed, accepted as the best answers we have for today, then published to the public. That is obviously not to say some of the formulas we have are permanent. They are the best we have at the time, but some formulas like root fluid mechanics and physics will stay the same pending some incredible Euler-like genius.

Dan Wilder

8/25/2025 08:15:04 am

Little digging but here ya go. IF I can find the reports from reputable links I'll post as a reply.

https://www.sfpe.org/publications/fpemagazine/fpeextra/etarchives/fpeetissue1

Dan Wilder

8/25/2025 08:58:46 am

As the info came from the Technical Committee, notes are not going to be easily available but below was the introduction of the section and formula.

https://docinfofiles.nfpa.org/files/AboutTheCodes/13/ROCA1999-13.pdf

Page 157-158

(Log #CP7)
13- 129- (5-2.3.2.3 (New)): Accept
SUBMITTER: Technical Committee on Automatic Sprinklers
RECOMMENDATION: Add a new section as follows:
"When listed quick response sprinklers are used throughout, the
system area of operation is permitted to be reduced without revising the density as indicated in Figure 5-2.3.2.3 when all of the following conditions are satisfied:
Wet pipe system
Light hazard or ordinary hazard occupancy
30 foot maximum ceiling height
The number of sprinklers in the design area shall never be less
than five."

Ceiling height (ft)
Figure 5-2.3.2.3

SUBSTANTIATION: A series of tests completed in 1989 indicated that on average, a smaller number of QR sprinklers tended to operate when compared to standard response sprinklers. While this phenomenon was documented, no credit or recognition was ever given for this. On average, QR sprinklers will operate sooner than standard response sprinklers in similar fire scenarios. This improves the fire control ability of the device and should provide marginal life safety benefits.
COMMITTE ACTION: Accept.
NUMBER OF COMMITTEE MEMBERS ELIGIBLE TO VOTE:27
VOTE ON COMMITTEE ACTION: AFFIRMATIVE: 27

Franck

8/25/2025 10:08:25 am

As indicated by Dan, Pete, Josh and Anthony, it is just a way to illustrate what was obtained from the tests. If with QR we have fewer sprinklers operating, then maybe we can adjust the design requirements.
To be honest, as an AHJ, I only use this one (as well as the one to reduce the design when using high temperature sprinklers with EH occupancies) only to evaluate existing systems or retrofit existing installations without too many changes. For new systems, if QR are used, I am very happy (they may perform better) but still recommend the design without QR.

Note that the same would apply to the curves for commodity classes. When making the tests in the 70s and 80s, they mostly tested class III and Gr A plastic occupancies and made extrapolations for the other curves (one or 2 tests and then draw a parralel line... more or less).

Jack G

8/25/2025 11:28:53 am

I go back to 1956. From what I recall, the committee didn’t use any testing, in 2007, when they added the qr reduction formula. They developed it from a concept that quicker activation could control the fire and use less water and make sprinklers more affordable.
That’s what I remember anyway.

James Art

8/27/2025 04:35:51 pm

NOTE the reduction in area is NOT permitted in CA for Ordinary Hazard, only for Light Hazard.
See the CA BC Chapter 35: NFPA 13, Amended Sections

This provides a better factor of safety in these Occupancies.
--------------------------------------------------------
Some history:
Reminds of the Los Angeles Fire Tests used to help establish NFPA 13D. ( The "D" may stand for Deficient? :-)

They had some buildings scheduled for demolition near the LA Airport, that they were able to use for fire testing of a new Grinnell Sprinkler with a very quick link. A modified Duraspeed, The first Residential Sprinkler.

They wanted to justify a 2 sprinkler design calculation
with a small water meter. Get the costs down.
So they installed a system, and provided used furniture to simulate a living room, with a couch, chair, end table and a small trash can and did some fire tests. There were two sprinklers in the living room, and one more in the adjacent entry way.

They had volunteer fire fighter students and hoses standing by.
The fire was started in the trash can, and spread to the couch,
and took off. The first sprinkler over the couch activated,
and seemed to help knock down the fire and smoke. Then the 2nd one, and soon the third, in the entryway.
With 3 sprinklers flowing, the pressure dropped, and all were "pissing in the wind". Poor distribution, droplet size, and the fire started to get much larger, so they brought in the hose team to save the building.
All on film.
The write up was very interesting: They said that had the third sprinkler not activated, the system would have been a success
and proposed repeating the test, with another couch, and the third sprinkler plugged!

In my mind, this was NOT a justification for a 2 sprinkler design, or for sprinklers at all!
IF you know WHERE a house fire will be, perhaps you also know WHEN. Just call me a couple of hours in advance, so I can come by with a bucket!

We now have much better residential sprinklers, that cover more area, with less water. AND we call 13D a "Life Safety System", designed only to help with exiting.
Many cities and AHJ's put an area limit like 5000 sq. ft. or other on the 2 sprinkler calc. Many require 13R, which is generally four sprinklers.

What is the Origin of the QR Reduction Formula?

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